## anonymous one year ago Hey guys. I need help on pre-cal. I don't really understand horizontal and vertical stretches besides the fact that "a stretch by a factor of c if c > 1" and "a shrink by a factor of c if c < 1" I will post the question below.

1. anonymous

2. zepdrix

Whenever you multiply y by something, it corresponds to a vertical stretch. Whenever you multiply x by something, it corresponds to a horizontal stretch.

3. zepdrix

Think of f(x) as y.

4. zepdrix

$\large\rm \color{orangered}{y=\sqrt x}$We achieve our new function multiplying both sides by 8,$\large\rm 8\color{orangered}{y}=8\color{orangered}{\sqrt x}$ If f(x) = y Then g(x) = 8y This is a vertical stretch of f(x) by a factor of 8. We manipulated the y.

5. zepdrix

It might be confusing the way I said that you're multiplying y by something. But remember that this $$\large\rm \sqrt{x}$$ is y. So when you multiply that by 8, you're multiplying y by 8, because that is y.

6. zepdrix

To make horizontal stretches, you multiply x by a value. Example:$\large\rm f(x)=\sqrt{x}\qquad\to\qquad g(x)=\sqrt{4x}$g(x) represents a horizontal stretch of f(x) by a factor of 4.

7. anonymous

Thank you so much! No, I understood you completely it was much easier understanding your explanation than the textbook's. Thank you. :)

8. zepdrix

yay \c:/